After the ODIs, England play three T20s against New Zealand before another three against India as their World Cup preparations ramp up.
Their World Cup campaign begins on 12 June against Sri Lanka at Edgbaston.
Key spinner Sophie Ecclestone, 27, also sat out Sunday’s win with a quad problem.
The camp has suggested Ecclestone’s injury is only minor, and she was seen in the gym at Chester-le-Street, but it is not clear if she will be fit for Wednesday. She has only played twice for Lancashire this season.
Captain Nat Sciver-Brunt is also missing the New Zealand ODIs because of a left calf tear. She is on course to return for the T20s against the White Ferns.
Should Wong’s issue be worse than feared, the situation is complicated further by a concussion suffered by all-rounder Em Arlott on Sunday.
The 28-year-old would be one of those best placed to take Wong’s place but, after being hit on the head while batting in the nets, has been ruled out of the New Zealand ODI series under concussion protocols.